Cambridge IGCSE™
* 0 0 6 9 1 8 1 7 1 1 *
MATHEMATICS
0580/23
October/November 2020
Paper 2 (Extended)
1 hour 30 minutes
You must answer on the question paper.
You will need:
Geometrical instruments
INSTRUCTIONS
●
Answer all questions.
●
Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
●
Write your name, centre number and candidate number in the boxes at the top of the page.
●
Write your answer to each question in the space provided.
●
Do not use an erasable pen or correction fluid.
●
Do not write on any bar codes.
●
You should use a calculator where appropriate.
●
You may use tracing paper.
●
You must show all necessary working clearly.
●
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
●
For r, use either your calculator value or 3.142.
INFORMATION
●
The total mark for this paper is 70.
●
The number of marks for each question or part question is shown in brackets [ ].
This document has 12 pages. Blank pages are indicated.
DC (KN/FC) 189269/2
© UCLES 2020
[Turn over
2
1
Write down the cube number that is greater than 50 but less than 100.
................................................. [1]
2
Calculate.
4
0.0025
................................................. [1]
3
In triangle ABC, BC = 7.6 cm and AC = 6.2 cm.
Using a ruler and compasses only, construct triangle ABC.
Leave in your construction arcs.
The side AB has been drawn for you.
A
B
[2]
4
Simplify.
a2 ' a6
................................................. [1]
© UCLES 2020
0580/23/O/N/20
3
5
Thor changes 40 000 Icelandic Krona into dollars when the exchange rate is 1 krona = $0.0099 .
Work out how many dollars he receives.
$ ................................................ [1]
6
A
NOT TO
SCALE
58°
B
82°
C
The diagram shows triangle ABC.
The triangle is reflected in the line BC to give a quadrilateral ABDC.
(a) Write down the mathematical name of the quadrilateral ABDC.
................................................. [1]
(b) Find angle ACD.
Angle ACD = ................................................ [2]
7
Change 457 000 cm2 into m2.
.............................................m2 [1]
© UCLES 2020
0580/23/O/N/20
[Turn over
4
8
The length, l cm, of a line is 18.3 cm, correct to the nearest millimetre.
Complete this statement about the value of l.
.................... G l 1 .................. [2]
9
1
1
Without using a calculator, work out 1 # 2 .
7
10
You must show all your working and give your answer as a mixed number in its simplest form.
................................................. [3]
10 Solve the simultaneous equations.
You must show all your working.
3x - 8y = 22
x + 4y = 4
x = ................................................
y = ................................................ [3]
© UCLES 2020
0580/23/O/N/20
5
11
A bag contains 7 red discs, 5 green discs and 2 pink discs.
(a) Helen takes one disc at random, records the colour and replaces it in the bag.
She does this 140 times.
Find how many times she expects to take a green disc.
................................................. [2]
(b) Helen adds 9 green discs and some pink discs to the discs already in the bag.
2
The probability of taking a green disc is now .
7
Find the number of pink discs that Helen added to the bag.
................................................. [2]
12 A straight line, l, has equation
y = 5x + 12 .
(a) Write down the gradient of line l.
................................................. [1]
(b) Find the coordinates of the point where line l crosses the x-axis.
( ....................... , ......................) [2]
(c) A line perpendicular to line l has gradient k.
Find the value of k.
k = ................................................ [1]
© UCLES 2020
0580/23/O/N/20
[Turn over
6
13
A
B
Use set notation to describe the shaded region.
................................................. [1]
14
N = 24 # 3 # 75
PN = K , where P is an integer and K is a square number.
Find the smallest value of P.
P = ................................................ [2]
15
m = 2p +
x
y
Make x the subject of this formula.
x = ................................................ [3]
© UCLES 2020
0580/23/O/N/20
7
16 A paperweight has height 4 cm and volume 38.4 cm3.
A mathematically similar paperweight has height 7 cm.
Calculate the volume of this paperweight.
.......................................... cm3 [3]
17 Adil and Brian are paid the same wage.
Adil is given a 7% pay decrease and his new wage is $427.80 .
Brian is given a 7% pay increase.
Work out Brian’s new wage.
$ ................................................ [3]
18 (a) Simplify.
`4xy 2j
3
................................................. [2]
25 = 125 k
(b)
Find the value of k.
k = ................................................ [1]
© UCLES 2020
0580/23/O/N/20
[Turn over
8
19
v + 10
Speed
(m/s)
NOT TO
SCALE
v
0
0
40
24
Time (seconds)
The diagram shows the speed–time graph for the final 40 seconds of a car journey.
At the start of the 40 seconds the speed is v m/s.
(a) Find the acceleration of the car during the first 24 seconds.
......................................... m/s2 [1]
(b) The total distance travelled during the 40 seconds is 1.24 kilometres.
Find the value of v.
v = ................................................ [4]
20 Factorise.
3x + 8y - 6ax - 16ay
................................................. [2]
© UCLES 2020
0580/23/O/N/20
9
21
B
NOT TO
SCALE
8 cm
30°
O
P
A
OAB is the sector of a circle, centre O.
OB = 8 cm and angle AOB = 30°.
BP is perpendicular to OA.
(a) Calculate AP.
AP = ........................................... cm [3]
(b) Work out the area of the shaded region APB.
.......................................... cm2 [3]
© UCLES 2020
0580/23/O/N/20
[Turn over
10
22 The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle.
Time (t seconds)
0 1 t G 10
10 1 t G 15
15 1 t G 20
20 1 t G 40
40 1 t G 75
9
18
22
30
21
Frequency
(a) Calculate an estimate of the mean time.
............................................... s [4]
(b) Emmanuel draws a histogram to show this information.
The table shows the heights, in cm, of some of the bars for this histogram.
Complete the table.
Time (t seconds)
0 1 t G 10
10 1 t G 15
15 1 t G 20
Height of bar (cm)
3.6
14.4
17.6
20 1 t G 40
40 1 t G 75
[3]
© UCLES 2020
0580/23/O/N/20
11
23 y is inversely proportional to the square root of x.
When y = 7 , x = 2.25 .
Write y in terms of x.
y = ................................................ [2]
24 Simplify.
x 2 - 25
x 2 - 17x + 60
................................................. [4]
Question 25 is printed on the next page.
© UCLES 2020
0580/23/O/N/20
[Turn over
12
25 Solve 3 tan x =- 4 for 0° G x G 360° .
x = .................. or x = ................... [3]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
0580/23/O/N/20